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O. Gil-Medrano and A. Montesinos Amilibia
About a Decomposition of the Space of Symmetric Tensors of Compact Support on a Riemannian Manifold
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| Published: |
July 13, 1994 |
| Keywords: |
manifold of Riemannian metrics, elliptic operators on non-compact manifolds, manifolds of maps |
| Subject: |
Primary: 58D15, 58D17. Secondary: 58G25 |
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Abstract
Let M be a noncompact manifold and let Γ∞c(S2(M))
(respectively Γ∞c(T1(M))) be the LF space of 2-covariant symmetric
tensor fields (resp. 1-forms) on M, with compact support. Given any Riemannian metric g on
M, the first-order differential
operator δ*:Γ∞c(T1(M))→Γ∞c(S2(M)) can be defined by
δ*ω = 2 symm∇ω, where ∇
denotes the Levi-Civita connection of g.
The aim of this paper is to prove that the subspace
Im δ* is closed and to show several examples of
Riemannian manifolds for which
Γ∞c(S2(M)) ≠ Im δ*
⊕ (Imδ*)⊥,
where orthogonal is taken with
respect to the usual inner product defined by the metric.
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| Author information
Departamento de Geometría y Topología. Facultad de
Matemáticas. Universidad de Valencia. 46100 Burjasot, Valencia. SPAIN.
Olga.Gil@uv.es
Angel.Montesinos@uv.es
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